We present resonant ultrasound elastic constant measurements of the clathrate compounds Eu8Ga16Ge30 and Sr8Ga16Ge30. The elastic response of the Eu clathrate provides clear evidence for the existence of a new type of four-well tunneling states, described by two nearly degenerate four level systems (FLS). The FLS's are closely linked with the fourfold split positions of Eu known from neutron diffraction density profiles. Using a realistic potential we estimate the tunneling frequencies and show that the energy gap between the two FLS's is of the same order as the Einstein oscillator frequency. This explains why the observed harmonic oscillator type specific heat is not modified by tunneling states. In addition the quadrupolar interaction of FLS's with elastic strains explains the pronounced depression observed in elastic constant measurements. In the case of the Sr clathrate, we show that the shallow dip in the elastic constant c44 is explained using the same type of quadrupolar interaction with a soft Einstein mode instead of a FLS. PACS numbers: 62.30.+d,66.35.+a Clathrate compounds are composed of polyhedral cages with 12-16 faces formed by Si, Ge or Ga atoms [1]. The oversized cages accommodate guest atoms like Ba, Sr, or Eu which exhibit large amplitude anharmonic motion. This leads to a strong scattering of acoustic phonons and a small thermal conductivity. In many cases the electrical conductivity remains high and the resulting large thermoelectric figure of merit has led to sustained interest in this class of compounds. The glass-like low temperature thermal conductivity [2,3] and ultrasound attenuation [4,5] have been interpreted as evidence for the existence of tunneling states. These are commonly discussed within a generic two well potential model leading to two level system (TLS). The thermal conductivity is more glass-like for clathrates with larger atomic displacement parameters (ADP) of the guest atoms. For the clathrates discussed here the ADP's are very large. The nuclear density map for Eu(2) in Eu 8 Ga 16 Ge 30 clearly shows the distinct symmetrically related four maxima, away from the cage center [6,7], leading to the fourfold split site model. Large static ADP for Sr(2), and considerably smaller for Ba(2), in Sr 8 Ga 16 Ge 30 and Ba 8 Ga 16 Ge 30 , respectively, point also to the split site model [3,6,8], although the nuclear density maps do not show distinct fourfold maxima.In this letter we present elastic constant measurements on X 8 Ga 16 Ge 30 (X = Eu, Sr) that show anomalies that cannot be naturally explained within a generic TLS model. Instead we propose two new models that we feel are physically appealing because they draw their inspiration from the nuclear density map results.For Eu 8 Ga 16 Ge 30 we introduce a four-well potential model with the proper symmetry of split sites that describes a rotor type tunneling motion. We show that for appropriate potential parameters two partially degenerate FLS's exist. This model explains both the specific heat and elastic anomalies and is co...

We report low-temperature thermal expansion ␣͑T͒ and magnetostriction ͑B͒ measurements on the filled skutterudite PrOs 4 Sb 12 in magnetic fields up to 18 T. This compound appears to be the first example of a Pr-based heavy-fermion (HF) superconductor. Superconductivity manifests in a double jump at T c1 = 1.82 K and T c2 = 1.72 K, as also observed in specific heat measurements. The pressure dependencies of the two transitions are calculated by means of the Ehrenfest relation. For B ഛ 3 T, the normal-state thermal expansion shows a pronounced minimum related to crystalline electric field (CEF) splitting of the Pr 3+ ions. At low temperatures, the thermal expansion is dominated by a nuclear spin contribution of the Pr ions. Furthermore, anomalies in ␣͑T͒ and ͑B͒ for 4.4 T ഛ B ഛ 15 T and T ഛ 1.3 K have made it possible to determine the boundary of an ordered phase in the B-T plane that is presumably associated with quadrupolar order.

We investigate the Kondo Lattice Model on 2D clusters using the Finite Temperature Lanczos Method. The temperature dependence of thermodynamic and correlations functions are systematically studied for various Kondo couplings JK. The ground state value of the total local moment is presented as well. Finally, the phase diagrams of the finite clusters are constructed for periodic and open boundary conditions. For the two boundary conditions, two different regimes are found for small JK/t, depending on the distribution of non-interacting conduction electron states. If there are states within JK around the Fermi level, two energy scales, linear and quadratic in JK, exist. The former is associated with the onsite screening and the latter with the RKKY interaction. If there are no states within JK around the Fermi level, the only energy scale is that of the RKKY interaction. Our results imply that the form of the electron density of states (DOS) plays an important role in the competition between the Kondo screening and the RKKY interaction. The former is stronger if the DOS is larger around the Fermi level, while the latter is less sensitive to the form of the DOS.

Electronic band structures for Ba 6 Ge 25 and Ba 4 Na 2 Ge 25 clathrates are calculated using linear muffin-tin orbital method within the local-density approximation. It is found that barium states strongly contribute to the density of states at the Fermi level and thus can influence the transport properties of the compounds. A sharp peak of the density of states is found just at the Fermi level. It is also shown that the shifting of barium atoms toward experimentally deduced split positions in Ba 6 Ge 25 produces a splitting of this peak which may be interpreted as a band Jahn-Teller effect. If the locking of the barium atoms at the observed structural phase transition is assumed, this reduction of the density of states at the Fermi level can account for the experimentally observed decrease of the magnetic susceptibility and electrical resistivity at the phase transition, and the values of density of states are in agreement with low-temperature specific-heat measurements and variation of superconducting transition temperature with pressure.

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